ManySpace Labs

Eighteen free labs that teach by touch. Each one is useful on its own — no account, no paywall, no interruption.

Mathematics

Derivative Visualizer The derivative is a limit you can watch: shrink h and see the secant become the tangent. Integral Explorer The definite integral is just area — tiled, summed, and refined until the rectangles disappear into it. Unit Circle Explorer Sine and cosine are not buttons on a calculator — they are the shadows of one point on one circle. Complex Plane Explorer A complex number is an arrow: how far (modulus) and which way (argument). Multiplication turns and stretches. Probability Lab One flip tells you nothing. A thousand flips tell you p. Flip the coin and watch luck average out. Bayes Lab A 95%-accurate test can still cry wolf 5 times out of 6. The crowd decides what a positive means — move the prior and watch. Eigen Explorer Most directions come out of a matrix bent. A few come out only stretched — turn v until you find them. Fourier Series Every repeating wave is a stack of pure sines. Add harmonics one at a time and watch a square wave assemble itself — bumps, ringing, and all.

Physics

Projectile Motion Lab Speed, angle, gravity — three knobs, one arc. Sweep them and find the angle that flies farthest. Orbit & Gravity Every launch buys a fate: too slow falls home, just right loops forever, too fast never returns. Aim the arrow and scrub the flight.

AI & ML

Gradient Descent Playground One walker, one bowl, one knob that matters. Find the step size that flies — and the one that explodes. Loss Function Explorer Every loss is an opinion about error: MSE panics at outliers, MAE counts calmly, log-loss fears confident mistakes. k-Means Visualizer Clustering is a loop, not an oracle: assign every point to its nearest center, move each center to its mean, repeat. Logistic Regression A straight line, a squash function, and two clouds of dots: draw the boundary by hand, then let gradient descent show you its own. Forward Pass Two inputs, three hidden neurons, one output — nothing hidden. Push an input and watch every neuron answer at once. Backpropagation The forward pass makes a prediction; backprop decides how much to blame each weight. Follow one blame path from loss to weight. Attention Visualizer Attention is a spotlight: each word decides how much of every other word to mix into itself. Tokenization Explorer Type a sentence and watch a simplified toy tokenizer split it into pieces: suffixes peel off, numbers become digits, and tokens turn out to be neither words nor characters.